Math Rules

Question 1

Divisibility Rules for Small Integers

Answer 1

Question 2

What makes an integer X a multiple of an integer A?

Answer 2

X has all the prime factors of A.

Question 3

Exponents: Base of 0 or 1

Answer 3

0 raised to ANY power = 0

1 raised to ANY power = 1

If x = x² then x = 0 or 1

Question 4

Exponents: Base of -1

Answer 4

(-1)^ODD = -1

(-1)^EVEN = 1

Question 5

Exponential terms with common bases

Answer 5

Multiplying terms: add the exponents

Dividing terms: subtract the exponents

Question 6

Anything raised to the Zero Power

Answer 6

Equals 1

EXCEPTION: 0⁰ = UNDEFINED

Question 7

Negative Exponents

Answer 7

Something with a negative exponent is just “one over” that same thing with a positive exponent

y^-X = 1/(y^X)

Question 8

Nested Exponents

Answer 8

Multiply Exponents

(a²)³ = a⁶

Question 9

How does the result change when fractions are multiplied by EVEN exponents?

Answer 9

< -1: Bigger

Between -1 and 0: Bigger

Between 0 and 1: Smaller

>1: Bigger

Question 10

How does the result change when fractions are multiplied by ODD exponents?

Answer 10

< -1: Smaller

Between -1 and 0: Bigger

Between 0 and 1: Smaller

>1: Bigger

Question 11

When the bases are identical and no other bases exist…

Answer 11

Drop the bases and rewrite the exponents as an equation

2^6w = 2^5w-5

6w = 5w-5

w = -5

Be careful if 0, 1, or -1 is (or could be) the base.

Question 12

% Change Forumla

Answer 12

= Change / Original

Question 13

Two operations that do NOT guarantee an integer answer/value even when starting wtih an integer

Answer 13

1. Division
2. Root

Question 14

Definition of an integer

Answer 14

Negative or positive whole number and zero

Question 16

Integers in a set (consecutive integers, consecutive multiples)

Answer 16

Conecutive Integers: (Last - First + 1)

Consecutive Multiples [(Last - First) / Increment] + 1

Question 17

Properties of evenly spaced set

Answer 17

1. The average (arithmetic mean) and median are equal to each other
   * Note: For a set with an odd number of evenly spaced integers, the median/average will always be a member of the set. For a set with an even number of evenly spaced integers, the median/average will NOT be a member of the set.*
2. The mean and median of the set are equal to the average of the First and Last terms.

Question 18

Sum of Consecutive Integers

Ex: Sum of positive integers up to 100, inclusive?

Answer 18

Sum of Evenly Spaced Set = Average x Number of Terms

Ex: Sum = Average x Number of Terms

Average (of Evenly Spaced Sets) = (First + Last)/2

Average = (1 + 100)/2 = 50.5

Number of Terms = (Last - First + 1)

Number of Terms = 100 - 1 + 1 = 100

Sum = 50.5 x 100 = 5050